Transparency for lines isn't supported, and so the alpha channel is lost when you save and load. A workaround is to use patch, which does support transparency.
However, one thing to watch out for with the 'thick line for glow' strategy is sharp turns, the line will overlap with itself making a little bright spot. You can see a few little overlaps in the sine wave, and some bigger ones in the sawtooth below. You could avoid this by actually making a region (e.g. using patch and FaceColor/FaceAlpha properties), but you'd need to compute how far to offset that region from the line in data co-ordinates...
x=linspace(0,2*pi,100);
y=sin(x);
clr = [.85 .325 .098];
plot(x,y,'Color',clr)
p=patch([x flip(x)],[y flip(y)],clr);
p.EdgeColor=clr;
p.FaceColor='none';
p.EdgeAlpha=.15;
p.LineWidth=7;
p.LineJoin='round'; % to make it similar to plot's default
ax=gca;
ax.Color=[.1 .1 .1];
ylim padded
figure
x=linspace(0,5*pi,11);
y=sin(x);
clf;hold on
clr = [.85 .325 .098];
plot(x,y,'Color',clr)
p=patch([x flip(x)],[y flip(y)],clr);
p.EdgeColor=clr;
p.FaceColor='none';
p.EdgeAlpha=.15;
p.LineWidth=7;
p.LineJoin='round';
ax=gca;
ax.Color=[.1 .1 .1];
ylim padded
